Basic Math Examples

$\frac{77}{15} \div \frac{7}{13} + \frac{1}{5}$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

$\frac{77}{15} \cdot \frac{13}{7} + \frac{1}{5}$

Step 1.2

Cancel the common factor of $7$ .

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Step 1.2.1

Factor $7$ out of $77$ .

$\frac{7 (11)}{15} \cdot \frac{13}{7} + \frac{1}{5}$

Step 1.2.2

Cancel the common factor.

$\frac{7 \cdot 11}{15} \cdot \frac{13}{7} + \frac{1}{5}$

Step 1.2.3

Rewrite the expression.

$\frac{11}{15} \cdot 13 + \frac{1}{5}$

Step 1.3

Combine $\frac{11}{15}$ and $13$ .

$\frac{11 \cdot 13}{15} + \frac{1}{5}$

Step 1.4

Multiply $11$ by $13$ .

$\frac{143}{15} + \frac{1}{5}$

Step 2

To write $\frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{143}{15} + \frac{1}{5} \cdot \frac{3}{3}$

Step 3

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{1}{5}$ by $\frac{3}{3}$ .

$\frac{143}{15} + \frac{3}{5 \cdot 3}$

Step 3.2

Multiply $5$ by $3$ .

$\frac{143}{15} + \frac{3}{15}$

Step 4

Combine the numerators over the common denominator.

$\frac{143 + 3}{15}$

Step 5

Add $143$ and $3$ .

$\frac{146}{15}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{146}{15}$

Decimal Form:

$9.7\overline{3}$

Mixed Number Form:

$9 \frac{11}{15}$